Longest Subarray With Equal Number of 0s and 1s

The task is to find the longest subarray in a binary array with an equal number of 0s and 1s. A naive approach involves using a nested loop to calculate the sum of subarrays while treating 0s as -1. If the cumulative sum of a subarray equals zero, the subarray has an equal number of 0s and 1s, and the length is updated. This approach has a time complexity of O(n^2), which is inefficient for larger arrays.

A more efficient approach uses a hash map and prefix sum technique, reducing time complexity to O(n). By treating 0s as -1, the problem is transformed into finding the longest subarray with a sum of 0. The hash map stores the first occurrence of each prefix sum. If a prefix sum repeats, it indicates a subarray with an equal number of 0s and 1s. The difference in indices gives the length of the subarray, and the maximum length is updated accordingly.

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